The parabolic equation describing the evolution of the gravitational field is derived from Einstein equation. The instability of metric leads to a geometric pattern of turbulence. Microscopic turbulent pulsations generate two kinds of matter with positive and negative energy density, respectively. It is shown that in the case of negative energy density parabolic equation leads to an equation of Schrödinger type
Inexpediency of use of probability of correct diagnostics as a quality indicator of diagnostic algorithm is shown. The new indicator - the prognostic strength based on Mahalanobis distance between classes is offered and studied. We have found asymptotic distribution of the prognostic strength; the way of testing of adequacy of its application has been specified. In a problem of testing of two simple hypotheses the prognostic strength connection is established with Hellinger distance
Linear estimators of the probability of density in the spaces of an arbitrary nature and particular cases – nuclear, histogram, the Fix-Hodges type estimates are introduced. Consistency and asymptotic normality of linear estimates are proved under natural conditions. It is shown that the probability of the area can be found by linear density estimates. A special case of a finite set are discussed, it was found that sample mode converges to the theoretical one
The article describes a software interface with the universal cognitive analytical system "Eidos-X++" ensuring the transformation of character, in particular – the numerical series in a form that is directly perceived by this system. As a result, the system can contain 3 statistical and 7 intellectual models of the series, which highlights the relationship between the characters or numbers in these lines. To reflect the relationships between the characters we used the same private and integral data of the automated system of cognitive analysis (ASC-analysis), and in the reflection of reasons-and-effect relationships between events in the real area that has not previously been used in the theory of numbers. The article provides a detailed numerical examples of such studies on the example of the identification of relationships between numbers that represent the decimal digits of the PI number, in the example we use one million digits of the PI number after the decimal point
In the article, the concentration rows of monocrystal strontium and led tungstates doped with neodymium are treated. Judd-Ofelt intensity parameters are calculated
The results of the research of stability of the model of neutrophilomonocytegenesis are shown in the article. With the criterion of Routh-Hurwitz it's calculated that the system of the differential equations of cells growing is asymptotically steady. Threshold values of parameters of model at which the system becomes unstable are defined
In this article we have investigated the solutions of Maxwell's equations, Navier-Stokes equations and the Schrödinger associated with the solutions of Einstein's equations for empty space. It is shown that in some cases the geometric instability leading to turbulence on the mechanism of alternating viscosity, which offered by N.N. Yanenko. The mechanism of generation of matter from dark energy due to the geometric turbulence in the Big Bang has been discussed
In this article, the solutions of Einstein's equations for empty space, describing the gravitational field near the Sunlike star have been investigated. We have accounted the own field of the star, the motion of the star around the galactic center, the motion of the galaxy relative to the center of the local supercluster and the expansion of the Universe. The resulting gravitational field near the star has a complex structure, which leads to large-scale geometric turbulence linking large and small scales in this problem
From a modern point of view we have discussed Kolmogorov’s researches in the axiomatic approach to probability theory, the goodness-of-fit test of the empirical distribution with theoretical, properties of the median estimates as a distribution center, the effect of "swelling" of the correlation coefficient, the theory of averages, the statistical theory of crystallization of metals, the least squares method, the properties of sums of a random number of random variables, statistical control, unbiased estimates, axiomatic conclusion of logarithmic normal distribution in crushing, the methods of detecting differences in the weather-type experiments
In this article we consider the problem of solvability oа second boundary value problem for the model equation in partial derivatives with involutive deviation in the lowest terms. The investigation is based on a variable separation method